Voltage Booster

An ideal sinusoidal AC voltage source $(\vec{V_S} = 10 \angle 0^\circ)$ is placed in series with a load which takes the form of an ideal current source $(\vec{I_L} = 20 \angle {-30^\circ})$ .

There is also a series voltage source $(\vec{V_B})$ , whose purpose is to maximize the voltage across the load terminals, subject to the following constraints:

• The load terminal voltage must lead the load current, but not by more than $40^\circ$
• Voltage source $(\vec{V_B})$ cannot source or consume active power

What is the maximum attainable load terminal voltage magnitude (to 3 decimal places)?